pointtransform {DAIME}

Transform points between stratigraphic height and time/age

Description

This function (1) takes times/ages and determines the stratigraphic heights that were deposited at said times/ages or (2) takes stratigraphic heights and determines their time/age of deposition.

This can be used to (1) reconstruct the age/time/stratigraphic height of single objects placed in the sediment (2) construct age models from deposition rates and (3) transform (isotope) ratios or percentages from stratigraphic height into time/age and vice versa (see examples).

Usage

pointtransform( points , xdep , ydep ,
  direction = 'time to height' , depositionmodel = 'piecewise linear deposition rate' ,
  hiatuslist = list() , unit = 'time per sediment', timetype='time')

Arguments

points

Vector containing points that are transformed. Whether the entries in points are interpreted as stratigraphic heights or as times/ages depends on the option direction and timetype.

xdep

Vector of strictly increasing real numbers

ydep

Vector of real numbers. xdep and ydep describe the deposition model, and how they are interpreted depends on the option depositionmodel (and when direction='height to time', also on the option unit). By default, xdep and ydep describe a piecewise linear deposition rate, i.e. deporate=approxfun(xdep,ydep). For more options on how to describe deposition models, see depositionmodel

direction

OPTIONAL, default is 'time to height'. Determines the direction of the transformation. Either 'time to height' (in which case the input given by points corresponds to ages/times) or 'height to time' (in which case the input of points corresponds to stratigraphic heights)

depositionmodel

OPTIONAL, default is 'piecewise linear deposition rate'. Either 'piecewise linear deposition rate', 'binned deposition rate', or 'age model'. Determines how the input of xdep and ydep is interpreted. Dependent on the choice of direction and depositionmodel, different restrictions on the input of ydep exist, for details and examples see the vignette (available via vignette('DAIME') or the error messages

hiatuslist

OPTIONAL, default is an empty list. List of hiatuses to be included into the transformation, only used when direction='height to time', e.g. the transformation is from stratigraphic height to time. A list, containing vectors of length two as elements. Every element in the list corresponds to a hiatus: hiatuslist[[i]][1] is the stratigraphic height of the i-th hiatus, and hiatuslist[[i]][2] is its duration

unit

OPTIONAL, default is 'sediment per time'. Only used when direction='height to time', e.g. the transformation is from stratigraphic height to time, and depositionmodel is 'piecewise linear deposition rate' or 'binned deposition rate'. Either 'sediment per time' or 'time per sediment'. Determines the unit of the (binned or piecewise linear) deposition rate. If unit='sediment per time', the deposition rate describes the deposition rate with which a given point in the section was deposited. If unit='time per sediment', the deposition rate describes the time needed to deposit one unit of sediment (also know as the inverse deposition rate)

timetype

OPTIONAL, default is "time". Either "time" or "age", determines whether input/output will be interpreted/given as time or age

Value

If timetype='time' a list containing:

time

Vector containing the times at which the stratigraphic heights in height were deposited

height

Vector containing stratigraphic heights that were deposited at the times given in time

report

A short summary of the task performed

If timetype='age' a list containing:

age

Vector containing the ages at which the stratigraphic heights in height were deposited

height

Vector containing stratigraphic heights that were deposited at the ages given in age

report

A short summary of the task performed

If direction='time to height', age/time is a duplicate of the input points, and height contains the stratigraphic heights that were deposited at the ages/times given by points.

If direction='height to time', height is a duplicate of the input points, and age/time contains the ages/times at which the stratigraphic height given by points were deposited.

Output of NA in a vector indicates that the transformation was unsuccessful. This happens when entries of points coincide with a hiatus or are not in the domain of definition of the deposition model.

Author(s)

Niklas Hohmann

References

Hohmann, Niklas. 2018. Quantifying the Effects of Changing Deposition Rates and Hiatii on the Stratigraphic Distribution of Fossils. <doi:10.13140/RG.2.2.23372.51841>

See Also

For an overview of the functions in the DAIME package and examples using stratigraphic data see the vignette (available via vignette('DAIME') )

patterntransform for the transformation of input rates (stratigraphic patterns into temporal patterns and vice versa)

patterntodepositionmodel to create deposition models based on sedimentary dilution/condensation of known patterns

strattotimepointbin, strattotimepointcont, timetostratpointbin, and timetostratpointcont for diverse (outdated) wrappers of pointtransform.

Examples

### Example 1: Determine age/stratigraphic height of single objects
##define deposition rate
my.xdep=seq(0,12,length.out=100)
my.ydep=splinefunH(x=c(0,2,4,6,8,10,12),y=c(1,5,6,1,0.5,1,6),m=c(0,1.5,-0.5,-0.5,0,0.5,0))(my.xdep)
#unit of deposition rate is sediment per time unit (default setting)
usedunit='sediment per time' #unit of deposition rate is sediment per time unit (default setting)
#Plot deposition rate (in stratigraphic height)
plot(my.xdep,my.ydep,type='l',main='Deposition Rate',xlab='Stratigraphic Height',ylab=usedunit,
  ylim=c(0,max(my.ydep)))
##at what time was the object found at stratigraphic height 9 deposited?
#using default setting for depositionmodel (depositionmodel = 'piecewise linear deposition rate')
pointtransform(points=9,xdep=my.xdep,ydep=my.ydep,direction='height to time', unit=usedunit) 
#change unit used
usedunit='time per sediment'
pointtransform(points=9,xdep=my.xdep,ydep=my.ydep,direction='height to time', unit=usedunit) 
#note how different the results are!
##Now, take deposition rate as deposition rate in time
##at what stratigraphic height will an object appear that was deposited at time 5?
pointtransform(points=5,xdep=my.xdep,ydep=my.ydep,direction='time to height') 
#The option "unit" is unused when transforming from time to height

### Example 2: Create Age models based on a deposition rate
##create an age model. Essentially transform many points, which then approximate the age model
stratheights=seq(min(my.xdep),max(my.xdep),length.out=1000) #many points to approx. age model
usedunit='sediment per time'
reslist=pointtransform(points=stratheights,xdep=my.xdep,ydep=my.ydep,
  direction='height to time',unit=usedunit)
reslist$report
agemodelage=reslist$time
agemodelheight=reslist$height
#plot age model
plot(agemodelage,agemodelheight,xlab='Time',ylab='Stratigraphic Height',
  main=paste('Age model based on deposition rate \n with unit',usedunit))
  
#create age model but with other units for sedimentn input
usedunit='time per sediment'
reslist=pointtransform(points=stratheights,xdep=my.xdep,ydep=my.ydep,
  direction='height to time',unit=usedunit)
reslist$report
agemodelage=reslist$time
agemodelheight=reslist$height
#plot age model (note the difference the setting of unit makes in terms of time 
#required to deposit the section!)
plot(agemodelage,agemodelheight,xlab='Time',ylab='Stratigraphic Height',
  main=paste('Age model based on deposition rate \n with unit',usedunit))

##create age model with a hiatus 1: height to time
stratigraphicheight=5 #strat. height of the hiatus
duration=10 #duration of the hiatus
my.hiatuslist=list(c(stratigraphicheight,duration)) #required input format for hiatuses
reslist=pointtransform(points=stratheights,xdep=my.xdep,ydep=my.ydep,
  direction='height to time',hiatuslist=my.hiatuslist)
reslist$report
agemodelage=reslist$time
agemodelheight=reslist$height
#!using default setting for unit (sediment per time) again!
plot(agemodelage,agemodelheight,xlab='Time',ylab='stratigraphic height')
#the gap corresponds to the hiatus

##create age model with a hiatus 2: time to height
my.xdep2=c(0,6,8,12)
my.ydep2=c(0,6,5,12)
plot(my.xdep2,my.ydep2,type='l',main='Age Model, not eroded',xlab='time',ylab='height')
reslist=pointtransform(points=stratheights,xdep=my.xdep2,ydep=my.ydep2,
  direction='time to height',depositionmodel='age model')
reslist$report
agemodelage=reslist$time
agemodelheight=reslist$height
plot(agemodelage,agemodelheight,xlab='Time',ylab='stratigraphic height'
  ,main='Age model, eroded (with hiatus)')

###Example 3: Transform (isotope) ratios
##define deposition rate
my.xdep3=seq(0,12,length.out=100)
my.ydep3=splinefunH(x=c(0,2,4,6,8,10,12),y=c(1,5,6,1,0.5,1,6),
  m=c(0,1.5,-0.5,-0.5,0,0.5,0))(my.xdep3)
#create fake (oxygen) isotope curves
samplelocation=seq(0,12,length.out=20) #where the samples are taken
isotoperatio=(-1)^(0:19) +0.2*0:19
plot(my.xdep3,my.ydep3,type='l',ylim=c(0,7),xlab='Stratigraphic Height',ylab='')
lines(samplelocation,isotoperatio,type='l',lwd=4)
legend('topleft',lwd=c(1,4),legend=c('Deposition rate','(Isotope) ratio'))
#transform only (!) sample locations, NOT values 
#again using the default setting for unit
reslist=pointtransform(points=samplelocation,xdep=my.xdep3,ydep=my.ydep3,
  direction='height to time')
#Isotope ratios in time 
plot(reslist$time,isotoperatio,type='l',xlab='Time',ylab='Isotope Ratio',lwd=4)